Define as , and . Prove by induction that
Let P(n) be the propositional statement for n>1 " "
The LHS of P(2) is 5^2-2^2=21 and the RHS if P(2) is 7(3)-10(0)=21. So P(2) is true.
Now assume that P(j) is true for all j<k. That is assume . Then by this assumption that P(j-1) can be written as
Now I'm kind of stuck. This is either going to take some sick algebra or I made a boo-boo.